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Consequently, a gravitational lens has no single focal point, but a focal line. The term "lens" in the context of gravitational light deflection was first used by O. J. Lodge, who remarked that it is "not permissible to say that the solar gravitational field acts like a lens, for it has no focal length". [11]
Angles involved in a thin gravitational lens system. As shown in the diagram on the right, the difference between the unlensed angular position β → {\displaystyle {\vec {\beta }}} and the observed position θ → {\displaystyle {\vec {\theta }}} is this deflection angle, reduced by a ratio of distances, described as the lens equation
An Einstein Ring is a special case of gravitational lensing, caused by the exact alignment of the source, lens, and observer. This results in symmetry around the lens, causing a ring-like structure. [2] The geometry of a complete Einstein ring, as caused by a gravitational lens. The size of an Einstein ring is given by the Einstein radius.
The main lens lies at redshift z = 0.222, with the inner ring at z = 0.609 with an Einstein radius R E = 1.43 ± 0.01" and magnitude m = 19.784 ± 0.006, the outer ring is at z ≲ 6.9 with R E = 2.07 ± 0.02" and magnitude m = 23.68 ± 0.09 [1] The lensing galaxy is also known as SDSSJ0946+1006 L1, with the nearer lensed galaxy as SDSSJ0946 ...
The geometry of gravitational lenses. In the following derivation of the Einstein radius, we will assume that all of mass M of the lensing galaxy L is concentrated in the center of the galaxy. For a point mass the deflection can be calculated and is one of the classical tests of general relativity.
Strong gravitational lensing is a gravitational lensing effect that is strong enough to produce multiple images, arcs, or Einstein rings. Generally, for strong lensing to occur, the projected lens mass density must be greater than the critical density, that is . For point-like background sources, there will be multiple images; for extended ...
The odd number theorem is a theorem in strong gravitational lensing which comes directly from differential topology. The theorem states that the number of multiple images produced by a bounded transparent lens must be odd .
The cosmic experiment envisioned by Wheeler could be described either as analogous to the interferometer experiment or as analogous to a double-slit experiment. The important thing is that by a third kind of device, a massive stellar object acting as a gravitational lens, photons from a source can arrive by two pathways.